As far as I am aware, Maryland is a strong at-will employment state, which means they can terminate you for any reason or no reason, with some fairly narrow exceptions I won't bother listing here because being drunk on the job isn't one of them.
Whether or not you receive unemployment benefits is a different question, but if you haven't filed for benefits AND been denied benefits yet then discussion of whether or not you can be denied benefits for being terminated due to intoxication on the job, and whether the employer failed to comply with any requirements under law for denying benefits in that situation, seems premature.